Average Thermal Energy of Non-linear Polyatomic Gas Molecule Calculator

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✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature [T]			+10% -10%
✖The Moment of Inertia along Y-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Y-axis.ⓘ Moment of Inertia along Y-axis [I_y]			+10% -10%
✖The Angular Velocity along Y-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.ⓘ Angular Velocity along Y-axis [ω_y]			+10% -10%
✖The Moment of Inertia along Z-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Z-axis.ⓘ Moment of Inertia along Z-axis [I_z]			+10% -10%
✖The Angular Velocity along Z-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.ⓘ Angular Velocity along Z-axis [ω_z]			+10% -10%
✖The Atomicity is defined as the total number of atoms present in a molecule or element.ⓘ Atomicity [N]			+10% -10%

✖Thermal Energy is the input heat energy to a given system. This input heat energy is converted into useful work and a part of it is wasted in doing so.ⓘ Average Thermal Energy of Non-linear Polyatomic Gas Molecule [Q_in]

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Formula

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Average Thermal Energy of Non-linear Polyatomic Gas Molecule

Formula

`"Q"_{"in"} = ((3/2)*"[BoltZ]"*"T")+((0.5*"I"_{"y"}*("ω"_{"y"}^2))+(0.5*"I"_{"z"}*("ω"_{"z"}^2)))+((3*"N")-6)*("[BoltZ]"*"T")`

Example

`"27.0348J"=((3/2)*"[BoltZ]"*"85K")+((0.5*"60kg·m²"*(("35degree/s")^2))+(0.5*"65kg·m²"*(("40degree/s")^2)))+((3*"3")-6)*("[BoltZ]"*"85K")`

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Average Thermal Energy of Non-linear Polyatomic Gas Molecule Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thermal Energy = ((3/2)*[BoltZ]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-6)*([BoltZ]*Temperature)
Q_in = ((3/2)*[BoltZ]*T)+((0.5*I_y*(ω_y^2))+(0.5*I_z*(ω_z^2)))+((3*N)-6)*([BoltZ]*T)
This formula uses 1 Constants, 7 Variables

Constants Used

[BoltZ] - Boltzmann constant Value Taken As 1.38064852E-23

Variables Used

Thermal Energy - (Measured in Joule) - Thermal Energy is the input heat energy to a given system. This input heat energy is converted into useful work and a part of it is wasted in doing so.
Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Moment of Inertia along Y-axis - (Measured in Kilogram Square Meter) - The Moment of Inertia along Y-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Y-axis.
Angular Velocity along Y-axis - (Measured in Radian per Second) - The Angular Velocity along Y-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.
Moment of Inertia along Z-axis - (Measured in Kilogram Square Meter) - The Moment of Inertia along Z-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Z-axis.
Angular Velocity along Z-axis - (Measured in Radian per Second) - The Angular Velocity along Z-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point.
Atomicity - The Atomicity is defined as the total number of atoms present in a molecule or element.

STEP 1: Convert Input(s) to Base Unit

Temperature: 85 Kelvin --> 85 Kelvin No Conversion Required
Moment of Inertia along Y-axis: 60 Kilogram Square Meter --> 60 Kilogram Square Meter No Conversion Required
Angular Velocity along Y-axis: 35 Degree per Second --> 0.610865238197901 Radian per Second (Check conversion here)
Moment of Inertia along Z-axis: 65 Kilogram Square Meter --> 65 Kilogram Square Meter No Conversion Required
Angular Velocity along Z-axis: 40 Degree per Second --> 0.698131700797601 Radian per Second (Check conversion here)
Atomicity: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_in = ((3/2)*[BoltZ]*T)+((0.5*I_y*(ω_y^2))+(0.5*I_z*(ω_z^2)))+((3*N)-6)*([BoltZ]*T) --> ((3/2)*[BoltZ]*85)+((0.5*60*(0.610865238197901^2))+(0.5*65*(0.698131700797601^2)))+((3*3)-6)*([BoltZ]*85)

Evaluating ... ...

Q_in = 27.0347960060603

STEP 3: Convert Result to Output's Unit

27.0347960060603 Joule --> No Conversion Required

FINAL ANSWER

27.0347960060603 ≈ 27.0348 Joule <-- Thermal Energy

(Calculation completed in 00.004 seconds)

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Home » Chemistry » Kinetic Theory of Gases » Equipartition Principle and Heat Capacity » Average Thermal Energy of Non-linear Polyatomic Gas Molecule

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Created by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

Prerana Bakli has created this Calculator and 800+ more calculators!

Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< 24 Equipartition Principle and Heat Capacity Calculators

Internal Molar Energy of Non-Linear Molecule

Go Molar Internal Energy = ((3/2)*[R]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2))+(0.5*Moment of Inertia along X-axis*(Angular Velocity along X-axis^2)))+((3*Atomicity)-6)*([R]*Temperature)

Average Thermal Energy of Non-linear Polyatomic Gas Molecule

Go Thermal Energy = ((3/2)*[BoltZ]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-6)*([BoltZ]*Temperature)

Average Thermal Energy of Linear Polyatomic Gas Molecule

Internal Molar Energy of Linear Molecule

Rotational Energy of Non-Linear Molecule

Go Rotational Energy = (0.5*Moment of Inertia along Y-axis*Angular Velocity along Y-axis^2)+(0.5*Moment of Inertia along Z-axis*Angular Velocity along Z-axis^2)+(0.5*Moment of Inertia along X-axis*Angular Velocity along X-axis^2)

Translational Energy

Go Translational Energy = ((Momentum along X-axis^2)/(2*Mass))+((Momentum along Y-axis^2)/(2*Mass))+((Momentum along Z-axis^2)/(2*Mass))

Rotational Energy of Linear Molecule

Go Rotational Energy = (0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2))

Vibrational Energy Modeled as Harmonic Oscillator

Go Vibrational Energy = ((Momentum of Harmonic Oscillator^2)/(2*Mass))+(0.5*Spring Constant*(Change in Position^2))

Average Thermal Energy of Non-linear polyatomic Gas Molecule given Atomicity

Go Thermal Energy given Atomicity = ((6*Atomicity)-6)*(0.5*[BoltZ]*Temperature)

Average Thermal Energy of Linear Polyatomic Gas Molecule given Atomicity

Go Thermal Energy given Atomicity = ((6*Atomicity)-5)*(0.5*[BoltZ]*Temperature)

Total Kinetic Energy

Go Total Energy = Translational Energy+Rotational Energy+Vibrational Energy

Specific Heat Capacity given heat capacity

Go Specific Heat Capacity = Heat Capacity/(Mass*Change in Temperature)

Internal Molar Energy of Non-Linear Molecule given Atomicity

Go Molar Internal Energy = ((6*Atomicity)-6)*(0.5*[R]*Temperature)

Internal Molar Energy of Linear Molecule given Atomicity

Go Molar Internal Energy = ((6*Atomicity)-5)*(0.5*[R]*Temperature)

Heat Capacity

Go Heat Capacity = Mass*Specific Heat Capacity*Change in Temperature

Molar Vibrational Energy of Non-Linear Molecule

Go Vibrational Molar Energy = ((3*Atomicity)-6)*([R]*Temperature)

Molar Vibrational Energy of Linear Molecule

Go Vibrational Molar Energy = ((3*Atomicity)-5)*([R]*Temperature)

Vibrational Energy of Non-Linear Molecule

Go Vibrational Energy = ((3*Atomicity)-6)*([BoltZ]*Temperature)

Vibrational Energy of Linear Molecule

Go Vibrational Energy = ((3*Atomicity)-5)*([BoltZ]*Temperature)

Heat Capacity given Specific Heat Capacity

Go Heat Capacity = Specific Heat Capacity*Mass

Number of Modes in Non-Linear Molecule

Go Number of Normal modes for Non Linear = (6*Atomicity)-6

Vibrational Mode of Non-Linear Molecule

Go Number of Normal modes = (3*Atomicity)-6

Vibrational Mode of Linear Molecule

Go Number of Normal modes = (3*Atomicity)-5

Number of Modes in Linear Molecule

Go Number of Modes = (6*Atomicity)-5

Average Thermal Energy of Non-linear Polyatomic Gas Molecule Formula

What is the statement of Equipartition Theorem?

The original concept of equipartition was that the total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium. Equipartition also makes quantitative predictions for these energies. The key point is that the kinetic energy is quadratic in the velocity. The equipartition theorem shows that in thermal equilibrium, any degree of freedom (such as a component of the position or velocity of a particle) which appears only quadratically in the energy has an average energy of 1⁄2kBT and therefore contributes 1⁄2kB to the system's heat capacity.

How to Calculate Average Thermal Energy of Non-linear Polyatomic Gas Molecule?

Average Thermal Energy of Non-linear Polyatomic Gas Molecule calculator uses Thermal Energy = ((3/2)*[BoltZ]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-6)*([BoltZ]*Temperature) to calculate the Thermal Energy, The Average thermal energy of non-linear polyatomic gas molecule is produced when a rise in temperature causes atoms and molecules to move faster and collide with each other. Thermal Energy is denoted by Q_in symbol.

How to calculate Average Thermal Energy of Non-linear Polyatomic Gas Molecule using this online calculator? To use this online calculator for Average Thermal Energy of Non-linear Polyatomic Gas Molecule, enter Temperature (T), Moment of Inertia along Y-axis (I_y), Angular Velocity along Y-axis (ω_y), Moment of Inertia along Z-axis (I_z), Angular Velocity along Z-axis (ω_z) & Atomicity (N) and hit the calculate button. Here is how the Average Thermal Energy of Non-linear Polyatomic Gas Molecule calculation can be explained with given input values -> 27.0348 = ((3/2)*[BoltZ]*85)+((0.5*60*(0.610865238197901^2))+(0.5*65*(0.698131700797601^2)))+((3*3)-6)*([BoltZ]*85).

FAQ

What is Average Thermal Energy of Non-linear Polyatomic Gas Molecule?

The Average thermal energy of non-linear polyatomic gas molecule is produced when a rise in temperature causes atoms and molecules to move faster and collide with each other and is represented as Q_in = ((3/2)*[BoltZ]*T)+((0.5*I_y*(ω_y^2))+(0.5*I_z*(ω_z^2)))+((3*N)-6)*([BoltZ]*T) or Thermal Energy = ((3/2)*[BoltZ]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-6)*([BoltZ]*Temperature). Temperature is the degree or intensity of heat present in a substance or object, The Moment of Inertia along Y-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Y-axis, The Angular Velocity along Y-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point, The Moment of Inertia along Z-axis of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about Z-axis, The Angular Velocity along Z-axis also known as angular frequency vector, is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point & The Atomicity is defined as the total number of atoms present in a molecule or element.

How to calculate Average Thermal Energy of Non-linear Polyatomic Gas Molecule?

The Average thermal energy of non-linear polyatomic gas molecule is produced when a rise in temperature causes atoms and molecules to move faster and collide with each other is calculated using Thermal Energy = ((3/2)*[BoltZ]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-6)*([BoltZ]*Temperature). To calculate Average Thermal Energy of Non-linear Polyatomic Gas Molecule, you need Temperature (T), Moment of Inertia along Y-axis (I_y), Angular Velocity along Y-axis (ω_y), Moment of Inertia along Z-axis (I_z), Angular Velocity along Z-axis (ω_z) & Atomicity (N). With our tool, you need to enter the respective value for Temperature, Moment of Inertia along Y-axis, Angular Velocity along Y-axis, Moment of Inertia along Z-axis, Angular Velocity along Z-axis & Atomicity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Thermal Energy?

In this formula, Thermal Energy uses Temperature, Moment of Inertia along Y-axis, Angular Velocity along Y-axis, Moment of Inertia along Z-axis, Angular Velocity along Z-axis & Atomicity. We can use 1 other way(s) to calculate the same, which is/are as follows -

Thermal Energy = ((3/2)*[BoltZ]*Temperature)+((0.5*Moment of Inertia along Y-axis*(Angular Velocity along Y-axis^2))+(0.5*Moment of Inertia along Z-axis*(Angular Velocity along Z-axis^2)))+((3*Atomicity)-5)*([BoltZ]*Temperature)

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